P v -p is disputed, so someone is wrong there. Also, if you have ever done a 10+ line proof or 10+ place truth table you know it is trivially (pun intended) easy to get those wrong.

I think the concept of a thought and what it is for a thought to be about something needs to be refined before we can say more about the second example. To begin with, if I see a dragonfly and mistake it for a fairy and then start to think about the fairy I saw, it isn't clear that I really am thinking about a fairy.